Disciplines such as engineering often need to determine the behavior of a physical system such as a machine or an electrical circuit under different conditions or at different times. For example, when designing a machine, an engineer may need to determine the physical properties of different parts of the machine to verify whether they meet some desired product standards. The engineer may, for example, need to determine the range of pressure or heat that different parts will sustain during operation and accordingly use appropriate materials for those parts. Moreover, the engineer may need to find the energy input and the energy output of the machine to determine its efficiency and whether that efficiency meets some efficiency standards.
In some cases, to test different designs of the physical system, an engineer may model the physical system. A model enables the engineer to predict the behavior of the machine under different conditions and with different designs, and accordingly find an optimum design at a preliminary stage without the need to build the machine.
In some physical systems, called fluid transport systems, a fluid flows in the system and transports with it one or more physical properties. In a refrigerator, for example, a refrigerant may flow through different parts of the system and transport with it physical properties such as heat. In some systems, the fluid may also transport other types of properties such as a trace material, water vapor, etc. An engineer may need to model the changes in the transported property. The engineer may, for example, need to find out how the concentration of energy or trace material changes in each part of the system.
Existing modeling systems, however, often fail to model some fluid transport systems under special conditions. One example is finding the changes in the transported property when the fluid flows relatively slowly or does not flow at all.